Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Semiclosed operators in Hilbert space

Author: William E. Kaufman
Journal: Proc. Amer. Math. Soc. 76 (1979), 67-73
MSC: Primary 47A05
MathSciNet review: 534392
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In a Hilbert space H, an operator C is semiclosed provided that there exists a bounded operator B on H, with range the domain of C, such that CB is bounded. The family of all such operators in H is the smallest family containing all closed operators and itself closed under any one of the following: (1) sums, (2) products, (3) strong limits on domains of closed operators. In fact, every algebraic combination of closed operators in H is the sum of two closed one-to-one operators with the same domain and closed ranges.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A05

Retrieve articles in all journals with MSC: 47A05

Additional Information

PII: S 0002-9939(1979)0534392-9
Keywords: Closed operator, semiclosed operator, Hilbert space, complete inner product space, operator ranges
Article copyright: © Copyright 1979 American Mathematical Society